Question

a 45 kg girl is bouncing on a trampoline. during a certain interval after she leaves t he surface of the trampoline, her kinetic energy decreases to 220 J from 420 J. how high does she rise during this interval neglect air resistance

Answer 1

The girl rises approximately 0.45 meters during this interval.

Step-by-step explanation:

To find the height the girl rises during this interval, we can use the principle of conservation of energy. The initial kinetic energy of the girl is 420 J, and the final kinetic energy is 220 J. Since kinetic energy is given by the equation KE = (1/2)mv^2, we can solve for the final velocity: 220 = (1/2)(45)v^2. Solving for v, we find that the final velocity is approximately 8.16 m/s.

Next, we can find the change in potential energy by using the equation ∆PE = mgh, where ∆PE is the change in potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height. Plugging in the values, we get 200 = (45)(9.8)h. Solving for h, we find that the girl rises approximately 0.45 meters during this interval.

Answer 2

Answer: Height = 0.45m

Step-by-step explanation:

According to the conservation of energy, When there are no interactions outside a system ie neglecting air resistance,The change in kinetic energy is equal to the change in potential energy in a closed system.

Therefore the kinetic energy decrease, the potential energy increases, and decreases for increase in Kinetic energy

an is represented by the formulae

ΔKinetic energy + ΔPotential energy = 0

ΔKinetic energy = -ΔPotential energy ( where negative sign represent decrease as kinetic energy increases.

ΔK.E=ΔP.E

420J- 220J= mgh

mass = 45kg

g =gravitational acceleration =9.8 m/s^2

200J = 45 X 9.8 X h

h = 200/45 x 9.8 /= 0.45m